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Scaling Property

  1. Jan 19, 2008 #1
    1. The problem statement, all variables and given/known data
    a system has the following property:
    Its response to a sum of inputs is the sum of its responses to the inputs.

    (a) Prove that the scaling property holds for any integer scaling factor
    (b) Prove that the scaling property holds for any rational scaling factor

    2. Relevant equations

    3. The attempt at a solution
    [tex]y_{n}(t)+...+y_{1}(t)+y_{0}(t) = x_{n}(t)+...+x_{1}(t)+x_{0}(t) [/tex]

    That's basically what it's saying, where y(t) is the response to the x(t). But I don't understand what it means by proving it, isn't it kind of trivial?
  2. jcsd
  3. Jan 19, 2008 #2


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    Homework Helper

    Isn't it saying y(xn + ... + x0) = y(xn) + ... + y(x0) ?
  4. Jan 19, 2008 #3
    Oh yeah, thanks. But still isn't it trivial to prove scaling for it?
  5. Jan 19, 2008 #4


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    Staff Emeritus
    Science Advisor

    Well, sometimes you are given easy problems! If you think it is trivial, go ahead and do it.
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